Basic properties
| Modulus: | \(3895\) | |
| Conductor: | \(3895\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3895.gc
\(\chi_{3895}(2,\cdot)\) \(\chi_{3895}(128,\cdot)\) \(\chi_{3895}(203,\cdot)\) \(\chi_{3895}(307,\cdot)\) \(\chi_{3895}(333,\cdot)\) \(\chi_{3895}(402,\cdot)\) \(\chi_{3895}(412,\cdot)\) \(\chi_{3895}(623,\cdot)\) \(\chi_{3895}(717,\cdot)\) \(\chi_{3895}(718,\cdot)\) \(\chi_{3895}(743,\cdot)\) \(\chi_{3895}(812,\cdot)\) \(\chi_{3895}(922,\cdot)\) \(\chi_{3895}(1017,\cdot)\) \(\chi_{3895}(1153,\cdot)\) \(\chi_{3895}(1238,\cdot)\) \(\chi_{3895}(1307,\cdot)\) \(\chi_{3895}(1332,\cdot)\) \(\chi_{3895}(1333,\cdot)\) \(\chi_{3895}(1427,\cdot)\) \(\chi_{3895}(1648,\cdot)\) \(\chi_{3895}(1742,\cdot)\) \(\chi_{3895}(1743,\cdot)\) \(\chi_{3895}(1837,\cdot)\) \(\chi_{3895}(1853,\cdot)\) \(\chi_{3895}(1922,\cdot)\) \(\chi_{3895}(1948,\cdot)\) \(\chi_{3895}(2048,\cdot)\) \(\chi_{3895}(2257,\cdot)\) \(\chi_{3895}(2263,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((3117,2871,1236)\) → \((-i,e\left(\frac{17}{18}\right),e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 3895 }(333, a) \) | \(1\) | \(1\) | \(e\left(\frac{179}{180}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{45}\right)\) |